Stem and Leaf Plot
A stem and leaf plot is a unique table where values of data are split into a stem and leaf. The first digit or digits will be written in stem and the last digit will be written in leaf.
|1.||What is Stem and Leaf Plot?|
|2.||How to Read Stem and Leaf Plot?|
|3.||How to Split a Stem and Leaf Plot?|
|4.||How to Construct Stem and Leaf Plot?|
|5.||Stem and Leaf Plot Examples|
|7.||FAQs on Stem and Leaf Plot|
What is Stem and Leaf Plot?
A stem and leaf plot is a way of organizing data into a form that makes it easy to observe the frequency of different types of values. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf.
A stem and leaf plot is represented in form of a special table where each first digit or digits of data value is split into a stem and the last digit of data in a leaf. This " | " symbol is used to show stem values and leaf value and it is called as stem and leaf plot key. For example, 46 is represented as 4 on the stem and 6 on the leaf and shown using stem and leaf plot key like this 4 I 6.
In the image given below, the stem values are listed one below the other in ascending order and the leaf values are listed left to right from the stem values in ascending order.
As the stem and leaf plot definition states,
6 I 7 ⇒ 6 on the stem and 7 on the leaf read as 67.
6 I 8 ⇒ 6 on the stem and 8 on the leaf read as 68.
9 I 0 ⇒ 9 on the stem and 0 on the leaf read as 90.
9 I 1 ⇒ 9 on the stem and 1 on the leaf read as 91.
9 I 8 ⇒ 9 on the stem and 8 on the leaf read as 98.
Stem and Leaf Plot With Decimals
We can use stem and leaf plots with decimals the same way we use for whole numbers. The stem and leaf plot key (" | ") helps us understand how the data is organized on the stem and leaf plot with decimals. For example, stem and leaf plot key 4 I 2 is 4.2. 4 on the stem and 2 on the leaf read as 4.2. The decimal part will show on the leaf side.
Stem and Leaf Plot Statistics
Finding the mean, median, and mode are a part of stem and leaf plot statistics. Let's understand with help of an example. Consider the following stem and leaf plot worksheet which shows 5 data values.
|3||2 2 5|
The data values are already in ascending order. They are 20, 32, 32, 35 and 41
Mean of the data = Sum of data values ÷ Total number of values = (20 + 32 + 32 + 35 + 41) ÷ 5 = 160 ÷ 5 = 32.
Mean = 32
Mode is the data value that frequently appears.
Mode = 32
Median = The middle value of the data.
Median = 32
Thus, calculating the stem and leaf plot statistics is very easy.
How to Read Stem and Leaf Plot?
The stem and leaf plot key helps us understand the data values. The stem is on the left and the leaf is on the right. If you combine the values of the stem and the leaves, you will get the data values. Let us interpret the following data after studying the stem and leaf plot.
|0||2 6 8|
(a) What are the leaf numbers for stem 2?
Observe the stem and leaf plot table. Look at the stem column on the left and locate stem 2. Then find the corresponding leaves on the right. The leaf numbers are 5 and 9.
(b) What are the data values for stem 2?
Observe the stem and leaf plot table. Identify the data values. The stem 2 means 20 and the leaf means 5 and 9. Combining the values of the stem and the leaves, we get the data values 25 and 29.
(c) What are the data values for stem 0?
The numbers on the leaves against the value 0 on the stem are 2, 6, and 8. Thus, the data values are 2, 6, and 8.
(d) List the data values greater than 15.
From stem value 1, we get the data values 15 and 17. From stem value 2, we get the data values 25 and 29. Hence, the data values greater than 15 are 17, 25, and 29.
How to Split a Stem and Leaf Plot?
The split stem and leaf plot separates each stem into many stems based on its frequency. We place the smaller leaves on the first part of the split stem and the larger leaves on the subsequent stems.
For example, let's consider a set of data that includes the scores of 7 students in their math test.
78, 82, 82, 90, 94, 81, 72
Data in ascending order 72, 78, 81, 82, 82, 90, 94
Stem and Leaf Plot:
|8||1 2 2|
Split Stem And Leaf Plot
Thus, the split stem and leaf plot is an ordinary stem and leaf plot with each instance of the stem-leaf shown separately. It represents the stem section as many entries like how it appears in the data values.
How to Construct Stem and Leaf Plot?
Follow the steps for constructing a stem and leaf plot.
- Step 1: Look at the data and find the number of digits. Classify them as 2 or 3 digit numbers.
- Step 2: Fix the stem and leaf plot key. For example, 3 I 5 = 35, and 15 I 2 is 152.
- Step 3: Identify the first digits as stems and the last digit as leaves.
- Step 4: Determine the range of the data, i.e. the lowest and the highest values among the data.
- Step 5: Draw a vertical line. Place the stem on the left column and the leaf on the right column.
- Step 6: List the stems in the stems column. Arrange it in ascending order starting from the lowest to the top.
- Step 7: Plot the leaves in the column against the stem from lowest to the highest horizontally.
Given below are some important notes related to stem and leaf plots. Have a look!
- If we plot data using stem and leaf and place it alongside the new data, we might be able to see a correlation between both the data and the frequency distribution of data.
- The stem and leaf plot key for three-digit numbers is represented as two digits in the stem and one digit in the leaf. For example, 45 | 6 = 456
- The mean, median, and mode of the given data can easily be calculated using stem and leaf plots.
Related Articles on Stem and Leaf Plot
Check out these interesting articles to know more about stem and leaf plot and its related topics.
Stem and Leaf Plot Examples
Example 1: Given below is the stem and leaf plot of the people who attended an election campaign from various places. Jim is trying to read the plot, but he has many doubts. Can you clarify them?
i) What are the data values of stem 2?
ii) How many values are less than 16?
Stem Leaf 1 4 4 6 2 3 8 3 2 4 0 1
Solution: i) Stem 2 has 2 leaves that are 3 and 8. Hence, the data values are 23 and 28.
ii) Looking for the corresponding leaf value of stem 1, we have 4, 4, and 6 in the leaf column. Thus, we find that the value less than 16 is 14 and it appears twice.
Therefore, i) 23 and 28 are the data values of stem 2.
ii) Two values are less than 16.
Example 2: Richard is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions?
i) What is the mode of the plot?
ii) What is the mean of the plot?
iii) Find the range.
Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.
Hence, mode = 54
ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958
To find the mean, we have to divide the sum by the total number of values.
Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42
iii) Range = the highest value - the lowest value = 91 - 12 = 79
FAQs on Stem and Leaf Plot
What is the Difference Between a Stem and Leaf Plot and a Histogram?
A stem and leaf plot is a way to plot data values where the data values are split into stems and leaves. Under stems, we write the starting digit or digits and in leaf, we write the end digit of value whereas a histogram is a graphical representation of data using rectangular bars to represent data values.
Why do we use a Stem and Leaf Plot?
A stem-and-leaf plot is also known as a stem-and-leaf display. It is a plot for showing quantitative data in a graphical and tabular format to assist in visualizing the shape of a distribution.
How do you Read a Stem and Leaf Plot?
A stem and leaf plot is a plot where each data value is split into a leaf (the last digit) and a stem (the other digits). For example, 12 on the stem and 7 on the leaf read like 127, and 127 is written according to stem and leaf plot key 12 I 7.
What is the Key in a Stem and Leaf Plot?
The stem and leaf plot is an interesting and special way to show data values. While reading a stem and leaf plot, we need to understand the key. The key symbol is" | " like this. It will guide you on how to read the other values and how to split the values in a stem and leaf plot. For example, the key on the value 48 is shown like this 4 | 8. This shows that the stem (4) is in the tens place and the leaf (8) is in the ones place.
What is Stem and Leaf Plot in Math?
A stem and leaf plot is a table used to display data. The 'stem' is shown on the left side of the table and shows the first digit or digits of data values. The 'leaf' is shown on the right side of the table and shows the last digit of the data value. For example, 443 and 447 can be shown together on a stem and leaf plot as 44 | 3,7. 44 is shown under a column of the stem and the last digits of both numbers, 3 and 7, shown under the leaf column.
How do you Plot a 3 Digit Number on a Stem and Leaf Plot?
To plot a 3 digit number on a stem and leaf plot we will write the starting two digits under the stem and the last digit of each value will come under the leaf. For example, 149 is the value so we will plot 14 under stem and 9 under the leaf. Let's take another example of 150 and 151, in this case, 15 will come one time under the stem, and 0 and 1 are the last digits they will come under the leaf and shown like this 0, 1.
How is a Stem and Leaf Plot Different than a Bar Graph?
The bar graphs are best for comparing two sets of data quickly. A stem and leaf plot is a method used to classify discrete or continuous variables. A stem and leaf plot is used to organize collected data and the bar graph is used to represent the data graphically.